This invention pertains to the field of interferometric profilometry or, more precisely, to the field of wavelength tuned phase-shifting interferometry. Specifically, the invention is directed to a system and method utilizing a tunable coherent light source for the simultaneous measurement of multiple reflective surfaces to obtain precise surface height (or phase) information from a set of phase-shifted superimposed interferograms.
Phase-shifting interferometry (PSI) has proven to be a highly accurate and efficient method for the measurement of reflective surfaces in a variety of applications including optical testing, surface profilometry, surface roughness estimation and surface displacement measurement. The fundamental concept of PSI is that the phase of an interferogram can be extracted accurately by acquiring a set of phase shifted interferograms (or intensity frames) with a constant phase shift between any two adjacent frames. The phase shifts can be produced either by changing the optical path difference (OPD) between the test and a reference surface, or by changing the measurement wavelength if the OPD is not zero or by changing the polarization of light. Thus, all types of PSI measurements rely on some mechanism to shift or change the phase of an interferogram in a regular and predictable manner.
Phase shift interferometers have been successfully used for many years for achieving surface topography measurements of single surfaces. One such system is disclosed in the U.S. Pat. No. 5,473,434 to DeGroot. In the system of this patent, the phase shifts are produced by an assembly which mechanically, physically displaces components of an interferometer to vary the length of the cavity.
The U.S. Pat. No. 4,594,003 to Sommargren also is directed to an interferometer method and system to provide a phase map representing the optical path differences between a reference surface and a single object surface. In the system disclosed in the Sommargren patent, the phase differences are produced by utilizing a diode laser light source, the wavelength of which is varied; so that the phase difference between the two wave fronts producing the interference pattern is modulated by a known amount. The modulated interference pattern then is sensed with an imaging device; and the signals are processed to provide the desired phase map.
The systems of the U.S. Pat. Nos. 4,594,003 and 5,473,434 described above are representative of systems which are capable of providing phase measurements where there is only one surface involved. Although constant phase shifts are required by PSI to measure a single reflective surface, the phase calculation errors for a single surface are relatively small or insignificant; so that these small errors may be ignored, in most applications. The reason for this is that only a few interferograms are needed to extract phases from a single interferogram. Algorithms for single surface PSI, using five frames or seven frames of interferograms with a 90° phase shift between adjacent frames, are most commonly used. The relatively small number of frames employed is such that even if non-linear shifts between adjacent frames exist, the errors produced are insignificant. For this reason, single surface interferometric methods and systems typically shift the wavelength of a laser light source (the coherent light source) by applying voltage increments of equal amounts, even though the actual phase shifts produced are not linear, that is, the frequency shift between any two adjacent intensity frames is not the same.
Recently, PSI has been applied to the measurement of parallel plane transparent objects with multiple reflective surfaces. Such objects include thin glass plates, thin silicon wafers, and the like. These new applications produce multiple interferograms superimposed on the recording plane (or detector) of the system. Consequently, PSI for parallel plane objects cannot employ production of the desired phase shifts by varying the OPD directly. The reason a simple variation of the OPD is insufficient is that the phase shift speeds (or signal frequencies) are the same for each superimposed interferogram; and it is unlikely that any phase algorithm can be devised to separate the individual signals and then assign them to their respective surfaces. As a result, phase shifts for parallel plane multiple reflective surfaces require the use of a wavelength shifting driving mechanism to take advantage of the fact that the phases of each of the interferograms in the superimposed interferograms shift at different speeds (or signal frequencies) during the acquisition.
New algorithms have been developed for such multiple surface applications to extract the phases of all individual interferograms from a set of intensity frames. These new algorithms require the acquisition of many more intensity frames (as compared to single surface measurements), and with more precise phase shifts, in order to separate every individual interferogram from superimposed signals of other interferograms.
A system for accomplishing the measurement of the front and back surface topography of transparent objects which have substantially parallel surfaces is disclosed in the U.S. Pat. No. 5,488,477 to DeGroot. A relatively complex mathematical determination is employed in this patent to separate interference contributions due to the multiple reflections of the two parallel surfaces of the object. Among the procedures which are required by this patent is the reversing of the orientation of the object between two successive interference measurements. This then is followed by mathematical calculations to provide the desired profiles of the two different surfaces. A significant disadvantage of the system and method disclosed in this patent is the requirement of the reversing of the orientation of the object between measurements. This physical removal and replacement of the object after it is reversed is, in and of itself, capable of introducing errors into the final results.
The U.S. Pat. No. 6,359,692 to DeGroot is directed to another method and system for profiling objects having multiple reflective surfaces. In the system and method of this patent, a phase-shifting algorithm using a Fourier transform, operating in conjunction with a Fizeau interferometer is designed to extract the phases of a selected one of the multiple interference patterns produced by the different surfaces of the object. The algorithm is designed to select the patterns for only one of the surfaces. The algorithm then must be changed in order to select corresponding patterns for the other of the surfaces, while rejecting the patterns for the first surface.
It should be noted that to measure objects with multiple reflective surfaces such as a transparent plate, the underlying algorithm which is used must have the ability to extract phases of an underlying interferogram from a set of intensity frames with superimposed interferograms. To accomplish this, in general, a large number of intensity frames are needed, especially in the case of measuring thin transparent plates (for example, having a thickness less than 1 mm). If a measuring system cannot produce enough intensity frames, the algorithm may lose its ability to separate an interferogram of interest from a set of superimposed interferograms.
A different algorithm, using least-square fitting techniques to separate the front surface, back surface and thickness of a plate in PSI, was reported by Okada et al. in 1990 in a paper in Applied Optics, Vol. 29, No. 22, 1 August 1990, pp. 3280 to 3285. The RMS errors of the measurement for the surface shape are I/50 wavelengths in his paper. This measurement accuracy, however, is very difficult to achieve. One reason is the positioning of both the calibration object and the measurement object must be done with high precision. Even though there is a theoretical accuracy to this level, such measurement accuracy has not been achieved in industrial applications. In addition, the high precision positioning requirements for accomplishing the types of results theoretically set forth in the Okada paper preclude the use of the Okada system and method in a production line operation.
The non-linear phase shift errors which have been tolerated with single surface PSI methods and systems cannot be tolerated in systems for measuring parallel plane transparent objects, as described above in the Okada article and the DeGroot U.S. Pat. Nos. 5,488,477 and 6,359,692. The reason such non-linear phase shift errors cannot be tolerated in the measurement of transparent objects with multiple reflective surfaces is that the phase shift speed for each underlying interferogram varies (or the signal frequency spreads), and it is unlikely that a phase algorithm can be devised to separate the individual signals and then assign them to their respective surfaces. For applications to efficiently and accurately measure multiple parallel surfaces of transparent objects, it is necessary to use a wavelength shifting driving mechanism which takes advantage of the fact that the phases of each of the interferograms in the set of superimposed interferograms shift at different speeds (or signal frequencies) during the acquisition. Algorithms for extracting the phases of all of the individual interferograms for a set of intensity frames require the acquisition of many more intensity frames (40 to 80, for example) as compared to single surface measurements (which typically use 5 to 7 intensity frames for acquisition), and with more precise phase shifts in order to separate every individual interferogram from superimposed signals. For the measurement of a transparent plate having an 800 μm thickness for example, in a practical system setup, at least eighty frames of superimposed interferograms are required to separate the individual interferograms. The phase shift errors result in ambiguities in the separation of the individual interferograms from the combined signals. The separating errors, in turn, result in large phase errors on each surface as the information from the various surfaces is now mixed in a complicated manner. As mentioned above, this problem is not encountered in the phase measurement of a single surface.
As an example, the phase shift from an interferometer with a wavelength tunable laser can be expressed as                               θ          ⁡                      (            t            )                          =                                            2              ⁢              π              ⁢                                                           ⁢                              L                ⁡                                  (                                      x                    ,                    y                                    )                                            ⁢                              Δλ                ⁡                                  (                  t                  )                                                                    λ              ⁡                              (                                  λ                  -                                      Δλ                    ⁡                                          (                      t                      )                                                                      )                                              .                                    (        1        )            where L is the optical path difference of the test surface and the reference mirror, λ is the initial measurement wavelength, and Δλ(t) is the wavelength change. The relationship between the phase shift θ(t) and the wavelength shift Δλ(t) is not linear. This is clearly shown in Equation (1). This implies that the phase shift between any two adjacent intensity frames is not a constant if the wavelength change is directly proportional to the time. Such phase shift variation is small when Δλ(t)<<λ<<L. For the measurement of a single reflective surface, only very small Δλ(t) is required to acquire several frames of interferograms. The non-linearity of this method can be neglected in this case even though (ideally) the phase calculation algorithm requires a constant phase shift.
The simultaneous measurement of multiple reflective surfaces, however, employs phase extraction algorithms that require a much greater wavelength shift Δλ(t) to acquire the necessary intensity information. These algorithms are also much more sensitive to the phase shift errors. Thus, the phase shift variation in Equation (1) may be large enough to induce a phase calculation error that is no longer negligible. For example, a setup for the measurement of a transparent parallel plate is as follows: λ=632.8 nm, OPD L=20 mm, total number of interferograms n=45, and a maximum wavelength shift of 1 nm.
Non-linear phase shift resulting from a linear wavelength change with time is an intrinsic feature of any wavelength shifting interferometer. In addition to non-linear phase shift caused by the wavelength change, there exist other factors which contribute to the overall phase shift response. For example, the wavelength change in some driving mechanisms is achieved by changing the length of a Piezoelectric transducer (PZT). The non-linear length change (or response) of the PZT propagates into the phase shift response directly. These additional error sources from currently available driving mechanisms actually result in much larger phase shift errors than those caused solely by wavelength changes themselves.
It is desirable to provide a system and method to linearize the overall phase shift driving mechanism for the measurement of multiple reflective surfaces which demand only small phase shift changes between intensity frames.